Solve the problem.
-The cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x) = 4x2 - 16x + 32. Find the number of automobiles that must be produced to minimize the cost.
A) 16 thousand automobiles
B) 4 thousand automobiles
C) 2 thousand automobiles
D) 8 thousand automobiles

Question

Quizplus · Accepted Answer

The function C(x) = 4x^2 - 16x + 32 is a quadratic function that opens upwards (since the coefficient of x^2 is positive). The minimum cost occurs at the vertex of the parabola. The x-coordinate of the vertex is given by -b/(2a), where a = 4 and b = -16. Thus, x = -(-16)/(2*4) = 2. Therefore, 2 thousand automobiles must be produced to minimize the cost.

Solve the Problem. -The Cost in Millions of Dollars for a Company to a Company